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Designers of architectural glass in the United States rely on model building codes and standards for definitions of load resistance (LR) and other factors pertinent to design. Unfortunatel...

Model building codes and standards in the United States find their bases in a probabilistic model of glass load resistance (LR). In general, architectural flat glass design predicated on t...

Many previous studies have been conducted to investigate wind-induced galloping of slender structures or structural members. While some recent studies have examined the particular problem of galloping involving coupling between vibration components about the principal axes, few occurrences of such vibrations of full-scale structures have been reported. This paper presents a comprehensive investigation that incorporates full-scale and wind tunnel experiments and an analytical formulation to study the galloping oscillation of a type of slender tower. The full-scale and wind tunnel experiments were conducted to assess the characteristics of the oscillations, their correlation with the wind characteristics, as well as the core parameters that influence the interaction between the tower and the wind. Based on the results from the experiments, a state-space model for coupled galloping of slender towers is formulated. This model enables the prediction of the susceptibility of a slender tower to galloping instability through an evaluation of the net damping resulting from the wind-structure interaction. The tower subjected to monitoring in the full-scale study is used as an example structure in an illustrative application of the analytical model.

In the past few decades, designers increasingly work on glazing projects across the world requiring the use of international glazing standards that often differ from the designer’s national code. Commonly specified international glazing standards include prEN16612, AS1288, and ASTM E1300. Each of these standards has a different approach to determine window glass strength. This paper explores one aspect of glazing design for insulating glass units, the method for estimating the load sharing between the lites comprising insulating glass units. Each glazing standard uses a different method for estimating load sharing and how the effects of environmental loads are incorporated into the estimation. Environmental loads include but are not limited to changes in atmospheric pressure, resulting from elevation, climatic, and temperature variations. Additionally, several iterative methods appear in technical literature that attempt to account for most known factors affecting insulating glass load sharing. Each of these methods addresses environmental loads differently with differing degrees of accuracy. This paper presents comparisons between the three glazing standards above and an iterative method for load sharing with environmental loads in double and triple glazed insulating glass units. The major factors varied in the investigation are insulating glass unit constructions, dimensions, glass lite thicknesses, air space thickness, temperature and pressure and atmospheric pressure changes due to elevation change. Pressure versus load sharing percentage curves are presented for select double and triple insulating glass unit constructions. Figures in this paper will show the load sharing trends of different similarly loaded insulating glass units due to varying the pressure differential between the air space(s) and atmospheric pressures. The results of this study will indicate differences between the load sharing methods and provide example scenarios where the methods produce similar and different estimates of insulating glass load sharing.

The authors performed an experimental study with weathered fully tempered monolithic glass loaded to failure under controlled conditions. The 14 specimens in the study originated from the northeastern United States. The specimens were loaded with monotonically increasing pressure until fracture occurred in accordance with the ASTM E997 test method. The recorded failure load time histories were converted to equivalent 3-s failure loads using a modified load-transformation-integration method that incorporates residual compressive surface stress. Variations of the residual compressive surface stress measurements are presented for each specimen, and the effect that the variations in residual compressive surface stress have on the equivalent 3-s failure load calculations are also explored. Equivalent 3-s failure loads are shown to be proportional to the measured residual compressive surface stress. The equivalent 3-s failure load is compared to the load resistance calculated using ASTM E1300, and the m...

ASTM E 1300-07 employs only two glass type factors to adjust the load resistance of annealed glass for heat treatment, one factor for heat-strengthened glass and one factor for tempered glass. The use of only two factors provides a simplistic approach that fails to utilize the full capacity of heat-treated glass. ASTM E 1300-07 differentiates heat-strengthened from fully tempered glass by the magnitude of the residual compressive surface stress resulting from the heat treating process. Furthermore, ranges of residual compressive surface stress are specified for both heat-strengthened and fully tempered glasses, suggesting the glass type factors should vary with the residual compressive surface stress. This article presents a rational method for determining the load resistance of heat-treated glass based on the residual compressive surface stress. A method incorporating previously accepted design principles with the addition of extensive data computation is advanced to calculate load resistance for heat-tr...

Currently, the ASTM design methodology to determine the load resistance of annealed window glass incorporates a probability distribution to model glass load resistance. A probability of 8 lites per 1,000 broken at the first occurrence of the design load was selected to match a load resistance consistent with a historical design factor of 2.5. The historical use of a factor relationship leads to the misconception that the design methodology follows an allowable stress procedure. The misconception has led to another common misconception among architects and engineers that a constant maximum principal stress exists, associated with the load resistance for any combination of lite thickness, aspect ratio, and surface area. This paper presents the relationship between the maximum principal stress in glass lites associated with their design loads for a probability of breakage of 8 lites per 1,000. The relationship clearly shows that the maximum principal stress is not constant for a single lite thickness for varying rectangular dimensions much less for all lite geometry combinations. A series of charts illustrates the trends in magnitude and location of the maximum principal stress as a function of lite thickness, aspect ratio, and surface area.

ASTM E1300-09 uses a glass failure prediction model (GFPM) to quantify the probability that a critical surface flaw with a certain location and orientation will initiate a facture in the glass for a given lite geometry and uniform design load. The nonfactored load charts in ASTM E1300-09 are calibrated to a GFPM probability of breakage of 8/1,000 (0.008) at the first occurrence of the design load. The GFPM probability of breakage only addresses the material properties of the annealed monolithic window glass and does not incorporate the probability of the occurrence of the design load. Because window glass is typically designed to resist wind loads, the probability of the occurrence of the design load was based on ASCE 7-05. Using a Monte Carlo simulation to evaluate the limit-state equation, this paper presents a procedure to quantify the probability of failure incorporating the probability of the wind load and the probability of the window glass load resistance from the GFPM for window glass lite...

Understanding fracture initiation and propagation from perforated wellbores is essential to designing a perforation scheme to achieve an efficient hydraulic fracture stimulation treatment. The effect of perforation design on hydraulic fracture propagation has been extensively studied using experimental and analytical methods. Because the experimental investigation of hydraulic fracture is complicated, expensive, and often returns limited results, numerical methods can be applied as an efficient way to simulate fracture propagation from perforations. An Extended Finite Element Method (XFEM) was used to develop a model to investigate the effects of various parameters on fracture propagation from a set of perforations. These parameters included perforation orientation, perforation length, stress anisotropy, and elastic properties of the formation. Fracture propagation patterns from the XFEM model were first matched against published experimental studies and exhibited good agreement. The model was then used to broaden the study of perforation effects. Results of the modeling proved the effects of perforation orientation and length on hydraulic fracture propagation pattern. Horizontal stress anisotropy and rock mechanical properties were observed to strongly influence fracture propagation. It was also observed that, when two or more perforations are positioned at different orientation angles at the same depth, a fracture tends to propagate from the less deviated perforation. In these cases, the more deviated perforation can develop a short fracture, following a propagating pattern that could be caused by stress shadowing/interference. Stress interference between two perforations positioned closely together results in either perforation breakdown or fracture propagating away from one another. The simulation results from this study offer methods to enhance perforation design for hydraulic fracture treatment, particularly in the case of high stress anisotropy and high uncertainty in a preferred fracture plane. Analyzing competing perforations suggests that a technique based on this concept can be applied when high uncertainty exists regarding the direction of the principal horizontal stresses through increasing perforation density.

Invaluable to both well stimulation and wellbore stability is the study of fracture initiation and propagation. The literature is rich with fracture tip phenomena theories. In particular, the effect of tip plasticity has been the subject of much debate. However, little has been done to investigate the effect of rock mass plasticity, a potential controlling factor in weak and compactible rocks. This paper advances a 3D dynamic computational model to replicate the growth of hydraulic fractures in elastoplastic rocks. The proposed model is based on a non-linear Finite Element formulation that couples solid deformation and fluid flow. Rock is treated as a work-hardening elastoplastic material whose plastic deformation can be found using an associated flow rule. This paper features a new computational method to find material tangent stiffness tensor in non-linear Finite Element Analysis. A meshing/remeshing scheme is employed to maintain a high mesh resolution and to reach infinite boundary effect while keeping simulation runtime reasonable. The model tested successfully against analytical solutions for pressurized cracks and radially growing hydraulic fractures. Due to the action of fracturing fluid pressure on fracture faces, normal stress increases on the fracture faces and a zone of tensile stress forms ahead of the fracture. The size of this zone dictates fracture growth rate. Due to plastic deformation, when subjected to loading, compared to elastic rocks, elastoplastic rocks experience less increase in normal stress on the fracture face and a smaller tensile zone. Combined with typically high permeability of compactible rocks, this results in slower fracture growth, larger fracture widths and higher fracture pressures. Another significant observation is that elastoplastic rocks can undergo shear localization, depending on rock properties, stress state and treatment conditions. This paper presents a unique method to account for rock mass plasticity during fracturing operations. It showcases a robust 3D computational non-linear Finite Element model with a concrete physical foundation. Simulation results are in agreement with both laboratory and field observations.